Apparatus of this kind has already been proposed; the individual sections of the tire are injected in separate stations of such apparatus. In particular, there is a station provided for the torus and another one for the tread sections. With such known apparatus transport devices were needed for effecting transfer from one station to the other. Transport devices of this type increased the construction cost, on one hand, and made the production of the tire complicated, on the other hand production was complicated by the fact that the external shells used are composed of a top and a bottom part which are movable only axially with respect to each other, and the removal of the partially cast or injected tires together with the core and the insertion of this unit into the next-following external shell was a troublesome operation.